In this paper, the solid isotropic material with penalization (SIMP) method [1]}, [2]}, [3]} is used to solve the topology optimization problems. Let \(0 \le x_e \le 1\)  be the decision variable associated with element \(e\)  in the ground mesh and \(\mathbf {x}\)  be the vector of such decision variables. Let \(\rho _e\)  be the pseudo-density of element \(e\) , and \(\mathbf {\rho }(\mathbf {x})\)  be the vector of such variables after sequentially applying to \(\mathbf {x}\) :
